This phenomenon is referred to as a waning moon. As the moon orbits around the Earth, the angle between the Earth, the moon, and the sun changes, causing the visible portion of the moon's surface to decrease gradually. Eventually, the moon appears as a thin crescent and then disappears completely during the new moon phase. After the new moon, the process starts again with the waxing moon, in which the illuminated portion gradually increases until it becomes a full moon.
